On the set of weighted least squares solutions of systems of convex inequalities. (English) Zbl 0565.65034

Iusem, A.; de Pierro, A.

Commentat. Math. Univ. Carol. 25, 667-678 (1984).

Authors’ summary: This paper studies the set of fixed points of a convex combination of projections of m fixed convex sets, or equivalently the set of weighted least squares solutions of a system of convex inequalities. It is proved that such set is the intersection of translates of the convex sets and that its interior is empty when the convex sets have empty intersection. For the case of a system of linear inequalities, the behavior of the set as a function of the right hand side and the coefficients of the convex combination is discussed.

Reviewer: J.Parida

MSC:

65K05	Numerical mathematical programming methods
90C25	Convex programming
52A05	Convex sets without dimension restrictions (aspects of convex geometry)
65F10	Iterative numerical methods for linear systems

Keywords:

convex inequalities; convex sets; projection; weighted least squares; set of fixed points